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Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences

Author

Listed:
  • Nannan Wu

    (Business School, Hohai University, Nanjing 211100, China)

  • Yejun Xu

    (Business School, Hohai University, Nanjing 211100, China)

  • D. Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
    Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

Abstract

An incomplete fuzzy preference framework for the Graph Model for Conflict Resolution (GMCR) is proposed to handle both complete and incomplete fuzzy preference information. Usually, decision makers’ (DMs’) fuzzy preferences are assumed to be complete fuzzy preference relations (FPRs). However, in real-life situations, due to lack of information or limited expertise in the problem domain, any DM’s preference may be an incomplete fuzzy preference relation (IFPR). An inherent advantage of the proposed framework for GMCR is that it can complete the IFPRs based on additive consistency, which is a special form of transitivity, a common property of preferences. After introducing the concepts of FPR, IFPR, and transitivity, we propose an algorithm to supplement IFPR, that is, to find an FPR that is a good approximation. To illustrate the usefulness of the incomplete fuzzy preference framework for GMCR, we demonstrate it using to a real-world conflict over water allocation that took place in the Zhanghe River basin of China.

Suggested Citation

  • Nannan Wu & Yejun Xu & D. Marc Kilgour, 2019. "Water allocation analysis of the Zhanghe River basin using the Graph Model for Conflict Resolution with incomplete fuzzy preferences," Sustainability, MDPI, vol. 11(4), pages 1-17, February.
    • Handle: RePEc:gam:jsusta:v:11:y:2019:i:4:p:1099-:d:207397
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    References listed on IDEAS

    as
    1. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    2. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    3. D. Marc Kilgour & Keith W. Hipel, 2005. "The Graph Model for Conflict Resolution: Past, Present, and Future," Group Decision and Negotiation, Springer, vol. 14(6), pages 441-460, November.
    4. Yu Chu & Keith W. Hipel & Liping Fang & Huimin Wang, 2015. "Systems methodology for resolving water conflicts: the Zhanghe River water allocation dispute in China," International Journal of Water Resources Development, Taylor & Francis Journals, vol. 31(1), pages 106-119, March.
    5. Kevin W. Li & Keith W. Hipel & D. Marc Kilgour & Donald Noakes, 2005. "Integrating Uncertain Preferences into Status Quo Analysis with Applications to an Environmental Conflict," Group Decision and Negotiation, Springer, vol. 14(6), pages 461-479, November.
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    Cited by:

    1. Shinan Zhao & Haiyan Xu, 2019. "A Novel Preference Elicitation Technique Based on a Graph Model and Its Application to a Brownfield Redevelopment Conflict in China," IJERPH, MDPI, vol. 16(21), pages 1-14, October.
    2. Feifei Jin & Lidan Pei & Huayou Chen & Reza Langari & Jinpei Liu, 2019. "A Novel Decision-Making Model with Pythagorean Fuzzy Linguistic Information Measures and Its Application to a Sustainable Blockchain Product Assessment Problem," Sustainability, MDPI, vol. 11(20), pages 1-17, October.
    3. Mohammad Ehteram & Samira Ghotbi & Ozgur Kisi & Ahmed EL-Shafie, 2019. "Application of a Coordination Model for a Large Number of Stakeholders with a New Game Theory Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(15), pages 5207-5230, December.

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